"Even if you reduce the rate to 28 percent … you would still have the inversion problem with countries like Ireland that have a 10 percent tax. So the answer is we have to address it here and now," he said in an interview with "Power Lunch."

Inversions, in which corporations merge with foreign companies in order to move their tax domiciles to countries with a more favorable tax structure, have become increasingly common. Nine deals have already been agreed to this year and more are under consideration.

The bill bars federal contracts from going to companies that do inversion deals.

Read MoreHow banks are cashing in on tax-evading mergers

"If you don't want to pay the taxes to sustain this government and this nation, why should you be profiting by this government's business by bidding on it? We want to give the advantage to American companies that are based here and have their employees here," Sen. Durbin told "Closing Bell" Tuesday.

Treasury Secretary Jack Lew has called for Congress to pass sweeping tax measures to stop inversions and thinks a corporate tax rate of 28 percent can be achieved by eliminating deductions and loopholes. The current rate is 35 percent.

Sen. Durbin said he's all for corporate tax reform, but said the flood of corporate tax inversions has to stop.

"If we're going to play this kind of scenario 'if there's any corporate tax rate in the world lower than the United States, ours is too high,' it's a race to the bottom. We won't be able to keep up with other countries with even lower corporate tax rates," he said.